Abstract

The LIBOR Markov-functional model is an efficient arbitrage-free pricingmodel suitable for callable interest rate derivatives. We demonstrate that theone-dimensional LIBOR Markov-functional model and the separable onefactorLIBOR market model are very similar. Consequently, the intuitionbehind the familiar SDE formulation of the LIBOR market model may beapplied to the LIBOR Markov-functional model.The application of a drift approximation to a separable one-factor LIBORmarket model results in an approximating model driven by a one-dimensionalMarkov process, permitting efficient implementation. For a given parameterisationof the driving process, we find the distributional structure of this modeland the corresponding Markov-functional model are numerically virtuallyindistinguishable for short maturity tenor structures over a wide variety ofmarket conditions, and both are very similar to the market model. A theoreticaluniqueness result shows that any accurate approximation to a separablemarket model that reduces to a function of the driving process is effectivelyan approximation to the analogous Markov-functional model. Therefore, ourconclusions are not restricted to our particular choice of driving process. Minordifferences are observed for longer maturities, nevertheless the modelsremain qualitatively similar. These differences do not have a large impacton Bermudan swaption prices.Under stress-testing, the LIBOR Markov-functional and separable LIBORmarket models continue to exhibit similar behaviour and Bermudanprices under these models remain comparable. However, the drift approximationmodel now appears to admit arbitrage that is practically significant.In this situation, we argue the Markov-functional model is a more appropriatechoice for pricing.